Question

The area of a circle is 81\[\pi \]. What is the circumference of the circle?
(A) 6\[\pi \]
(B) 12\[\pi \]
(C) 18\[\pi \]
(D) 24\[\pi \]
(E) 36\[\pi \]

Answer 1

Hint: We need to assume a variable and assign it to the radius of the circle. After taking radius as a variable we need to formulate an equation according to the information given in the question. We are seeking to find the value of the variable corresponding to the radius.
If r is the radius of a circle, then we know that the formula for the circumference of the circle is 2\[\pi \] r and the area of the circle is \[\pi {r^2}\] .

Complete step-by-step solution:
Let, the radius of the circle is x.
Then the area of the circle is \[\pi {{\text{x}}^2}\].
According to the question, the area of the circle is 81\[\pi \].
\[\pi {{\text{x}}^2} = 81\pi \]
\[\Rightarrow {{\text{x}}^2} = 81\]
\[\Rightarrow {\text{x = 9}}\][as radius of a circle x cannot be negative]
Hence, the radius of the circle is 9 .
So, the circumference of the circle is, \[{\text{2}}\pi \times 9\] = 18\[\pi \].
Hence, among all of the options, option - (C) is correct.

Note: Students may confuse the area and circumference of a circle. So, be careful while using the formula of circumference and area. And also remember that, the radius of a circle is a positive value-it cannot be negative. Also, the radius cannot be zero as it will give a point.